The next step if to check that \(\sigma ^2>0\) . To this end we call upon the following representation of \(\sigma ^2\)  (see Section 17.4.3 of [1]}). Writing, for simplitcity, \(\tau (e)\)  for \(\tau _1(e)\) ,
\(\sigma ^2 = \pi (e)\mathbb {E}_e\left[\left(\sum _{n=1}^{\tau (e)}\bar{f}(X_n)\right)^2\right].\) 
